1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differential Geometry/notation help

  1. Apr 18, 2012 #1
    1. The problem statement, all variables and given/known data

    I have this theorem which I am having trouble understanding due to notation.

    Theorem: Define S,S'[itex]\subseteq[/itex]ℝ3 to be surfaces. Let f:S→S' be a smooth map. f is a local isometry if for all p in S, and all w1,w2 in TpS,
    <w1,w2>=<dfp(w1),dfp(w2)>.


    The thing I don't get, is what does dfp(w1) mean?
    What action is going on between dfp and w1?


    Thank you for your time.
     
  2. jcsd
  3. Apr 18, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    [itex]df_p[/itex] is the derived mapping from the tangent space at p in S to the tangent space at f(p) in S'.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook